Teaching and Learning Hyperbolic Functions (IV); Sums and Differences of Inverse Hyperbolic Functions

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Year:
2020
Type of Publication:
Article
Keywords:
Hyperbolic Sine, Hyperbolic Cosine, Hyperbolic Tangent, Hyperbolic Cotangent, Hyperbolic Secant, Hyperbolic Cosecant
Authors:
Teodor Dumitru Valcan
Journal:
IJISM
Volume:
8
Number:
5
Pages:
198-251
Month:
September
ISSN:
2347-9051
Abstract:
In three recent papers with the same generic name as this one and numbered with (I), (II) respectively (III), I presented the definitions, the consequences immediate resulting from these and a series of 38 properties of hyperbolic functions, properties that we divided into four groups, as follows: A) “Trigonometric” properties - nine properties; B) The derivatives of hyperbolic functions - six properties; C) The primitives (indefinite integrals) of hyperbolic functions – six properties and D) the monotony and the invertibility of hyperbolic functions - 17 properties. That in paper (I). In paper (II) I continued this approach and I presented another 54 properties of these functions, properties that have divided into three groups, as follows: E) Other properties “trigonometric” - 42 properties; F) Immediate properties of the inverse of hyperbolic functions – six properties and G) The derivatives of the inverse of hyperbolic functions - six properties. In paper (III) also I continued this approach and I presented another 36 properties of these functions, properties that we will divide into three groups, as follows: H) Properties “integral” and rewithrrence formulas - 11 properties; I) Relations between the inverse of hyperbolic functions - five properties and J) Relations between the hyperbolic functions and the inverses of other hyperbolic functions - 20 properties. In this paper we will continue this approach and will present and prove another 32 properties of these functions, properties that properties that we will classify them in the same group K): Sums and differences of inverse hyperbolic functions.

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